Bernoulli Distribution
In probability theory and statistics, the Bernoulli distribution, named after Swiss scientist Jacob Bernoulli, is the probability distribution of a random variable which takes value 1 with success probability p and value 0 with failure probability q=1-p.
Some problems in probability involve observing whether a specified event occurs. Noted as a “success” or a “failure”
Theory
If X is a random variable with this distribution, we have:
| X | 0 | 1 |
|---|---|---|
| p(x) | 1-p | p |
The probability mass funtion f of this distribution is as follows:
Examples
- Toss a coin: Ω = {H, T}
- Throw a fair die: Ω = {face value is a six, face value is not a six}
- Sent a message through a network and record whether or not it is received: Ω ={successful transmission, unsuccessful transmission}